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Equation 1 · Water Before Demography

What does this equation mean?

ΔP=(B−D)+M\Delta P = (B - D) + M

Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.

Inputs and operations(B - D) + M
Result or conditionΔ P
How to read the two sides of this formula. Follow the article passage for the meaning of each quantity.

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

Read it piece by piece

ΔP\Delta P

Symbol Δ P

Δ P is part of the quantity the equation computes from the expression on the right.

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BB

Symbol B

B is one of the signed contributions combined to compute the quantity on the left.

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DD

Symbol D

D is one of the signed contributions combined to compute the quantity on the left.

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MM

Symbol M

M is one of the signed contributions combined to compute the quantity on the left.

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=

=

The expressions on both sides represent the same quantity under the stated assumptions.

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addition

addition

Add the term after the plus sign to the term or group before it.

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subtraction

subtraction

Subtract the following term or group from the preceding one. A leading minus marks a negative quantity.

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change

change

Capital delta attached to a quantity marks a difference between two values of that quantity; the article’s sign convention determines the order.

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How to interpret it

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What the article says around this equation

For most of the period in which Europeans kept parish records, the largest towns buried more people than they baptised. Population still rose, which means the arithmetic was closed from outside. The identity is trivial but it is worth writing down, because almost every disagreement in this field is a disagreement about one of its terms: ΔP=(B−D)+M\Delta P = (B - D) + M. Population change in a city equals natural increase, births minus deaths, plus net in-migration. The urban graveyard claim is the specific and testable assertion that for long stretches the first bracket was negative while the sum was positive: cities grew, and grew only because the countryside kept sending replacements.

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Sources cited in the article section

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